# Properties

 Modulus 4011 Structure $$C_{570}\times C_{2}\times C_{2}$$ Order 2280

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(4011)

pari: g = idealstar(,4011,2)

## Character group

 sage: G.order()  pari: g.no Order = 2280 sage: H.invariants()  pari: g.cyc Structure = $$C_{570}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{4011}(19,\cdot)$, $\chi_{4011}(190,\cdot)$, $\chi_{4011}(2675,\cdot)$

## First 32 of 2280 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

orbit label order primitive -1 1 2 4 5 8 10 11 13 16 17 19
$$\chi_{4011}(1,\cdot)$$ 4011.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4011}(2,\cdot)$$ 4011.ci 570 yes $$-1$$ $$1$$ $$e\left(\frac{203}{570}\right)$$ $$e\left(\frac{203}{285}\right)$$ $$e\left(\frac{85}{114}\right)$$ $$e\left(\frac{13}{190}\right)$$ $$e\left(\frac{29}{285}\right)$$ $$e\left(\frac{59}{114}\right)$$ $$e\left(\frac{89}{95}\right)$$ $$e\left(\frac{121}{285}\right)$$ $$e\left(\frac{301}{570}\right)$$ $$e\left(\frac{256}{285}\right)$$
$$\chi_{4011}(4,\cdot)$$ 4011.ce 285 no $$1$$ $$1$$ $$e\left(\frac{203}{285}\right)$$ $$e\left(\frac{121}{285}\right)$$ $$e\left(\frac{28}{57}\right)$$ $$e\left(\frac{13}{95}\right)$$ $$e\left(\frac{58}{285}\right)$$ $$e\left(\frac{2}{57}\right)$$ $$e\left(\frac{83}{95}\right)$$ $$e\left(\frac{242}{285}\right)$$ $$e\left(\frac{16}{285}\right)$$ $$e\left(\frac{227}{285}\right)$$
$$\chi_{4011}(5,\cdot)$$ 4011.bs 114 yes $$1$$ $$1$$ $$e\left(\frac{85}{114}\right)$$ $$e\left(\frac{28}{57}\right)$$ $$e\left(\frac{47}{57}\right)$$ $$e\left(\frac{9}{38}\right)$$ $$e\left(\frac{65}{114}\right)$$ $$e\left(\frac{23}{114}\right)$$ $$e\left(\frac{37}{38}\right)$$ $$e\left(\frac{56}{57}\right)$$ $$e\left(\frac{7}{57}\right)$$ $$e\left(\frac{49}{114}\right)$$
$$\chi_{4011}(8,\cdot)$$ 4011.ca 190 no $$-1$$ $$1$$ $$e\left(\frac{13}{190}\right)$$ $$e\left(\frac{13}{95}\right)$$ $$e\left(\frac{9}{38}\right)$$ $$e\left(\frac{39}{190}\right)$$ $$e\left(\frac{29}{95}\right)$$ $$e\left(\frac{21}{38}\right)$$ $$e\left(\frac{77}{95}\right)$$ $$e\left(\frac{26}{95}\right)$$ $$e\left(\frac{111}{190}\right)$$ $$e\left(\frac{66}{95}\right)$$
$$\chi_{4011}(10,\cdot)$$ 4011.cg 570 no $$-1$$ $$1$$ $$e\left(\frac{29}{285}\right)$$ $$e\left(\frac{58}{285}\right)$$ $$e\left(\frac{65}{114}\right)$$ $$e\left(\frac{29}{95}\right)$$ $$e\left(\frac{383}{570}\right)$$ $$e\left(\frac{41}{57}\right)$$ $$e\left(\frac{173}{190}\right)$$ $$e\left(\frac{116}{285}\right)$$ $$e\left(\frac{371}{570}\right)$$ $$e\left(\frac{187}{570}\right)$$
$$\chi_{4011}(11,\cdot)$$ 4011.br 114 yes $$1$$ $$1$$ $$e\left(\frac{59}{114}\right)$$ $$e\left(\frac{2}{57}\right)$$ $$e\left(\frac{23}{114}\right)$$ $$e\left(\frac{21}{38}\right)$$ $$e\left(\frac{41}{57}\right)$$ $$e\left(\frac{11}{57}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{4}{57}\right)$$ $$e\left(\frac{1}{114}\right)$$ $$e\left(\frac{89}{114}\right)$$
$$\chi_{4011}(13,\cdot)$$ 4011.cc 190 no $$-1$$ $$1$$ $$e\left(\frac{89}{95}\right)$$ $$e\left(\frac{83}{95}\right)$$ $$e\left(\frac{37}{38}\right)$$ $$e\left(\frac{77}{95}\right)$$ $$e\left(\frac{173}{190}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{99}{190}\right)$$ $$e\left(\frac{71}{95}\right)$$ $$e\left(\frac{51}{190}\right)$$ $$e\left(\frac{17}{190}\right)$$
$$\chi_{4011}(16,\cdot)$$ 4011.ce 285 no $$1$$ $$1$$ $$e\left(\frac{121}{285}\right)$$ $$e\left(\frac{242}{285}\right)$$ $$e\left(\frac{56}{57}\right)$$ $$e\left(\frac{26}{95}\right)$$ $$e\left(\frac{116}{285}\right)$$ $$e\left(\frac{4}{57}\right)$$ $$e\left(\frac{71}{95}\right)$$ $$e\left(\frac{199}{285}\right)$$ $$e\left(\frac{32}{285}\right)$$ $$e\left(\frac{169}{285}\right)$$
$$\chi_{4011}(17,\cdot)$$ 4011.ck 570 yes $$1$$ $$1$$ $$e\left(\frac{301}{570}\right)$$ $$e\left(\frac{16}{285}\right)$$ $$e\left(\frac{7}{57}\right)$$ $$e\left(\frac{111}{190}\right)$$ $$e\left(\frac{371}{570}\right)$$ $$e\left(\frac{1}{114}\right)$$ $$e\left(\frac{51}{190}\right)$$ $$e\left(\frac{32}{285}\right)$$ $$e\left(\frac{61}{285}\right)$$ $$e\left(\frac{199}{570}\right)$$
$$\chi_{4011}(19,\cdot)$$ 4011.cf 570 no $$1$$ $$1$$ $$e\left(\frac{256}{285}\right)$$ $$e\left(\frac{227}{285}\right)$$ $$e\left(\frac{49}{114}\right)$$ $$e\left(\frac{66}{95}\right)$$ $$e\left(\frac{187}{570}\right)$$ $$e\left(\frac{89}{114}\right)$$ $$e\left(\frac{17}{190}\right)$$ $$e\left(\frac{169}{285}\right)$$ $$e\left(\frac{199}{570}\right)$$ $$e\left(\frac{49}{285}\right)$$
$$\chi_{4011}(20,\cdot)$$ 4011.by 190 yes $$1$$ $$1$$ $$e\left(\frac{87}{190}\right)$$ $$e\left(\frac{87}{95}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{71}{190}\right)$$ $$e\left(\frac{147}{190}\right)$$ $$e\left(\frac{9}{38}\right)$$ $$e\left(\frac{161}{190}\right)$$ $$e\left(\frac{79}{95}\right)$$ $$e\left(\frac{17}{95}\right)$$ $$e\left(\frac{43}{190}\right)$$
$$\chi_{4011}(22,\cdot)$$ 4011.cb 190 no $$-1$$ $$1$$ $$e\left(\frac{83}{95}\right)$$ $$e\left(\frac{71}{95}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{59}{95}\right)$$ $$e\left(\frac{78}{95}\right)$$ $$e\left(\frac{27}{38}\right)$$ $$e\left(\frac{4}{95}\right)$$ $$e\left(\frac{47}{95}\right)$$ $$e\left(\frac{51}{95}\right)$$ $$e\left(\frac{129}{190}\right)$$
$$\chi_{4011}(23,\cdot)$$ 4011.ci 570 yes $$-1$$ $$1$$ $$e\left(\frac{113}{570}\right)$$ $$e\left(\frac{113}{285}\right)$$ $$e\left(\frac{49}{114}\right)$$ $$e\left(\frac{113}{190}\right)$$ $$e\left(\frac{179}{285}\right)$$ $$e\left(\frac{89}{114}\right)$$ $$e\left(\frac{94}{95}\right)$$ $$e\left(\frac{226}{285}\right)$$ $$e\left(\frac{541}{570}\right)$$ $$e\left(\frac{106}{285}\right)$$
$$\chi_{4011}(25,\cdot)$$ 4011.bo 57 no $$1$$ $$1$$ $$e\left(\frac{28}{57}\right)$$ $$e\left(\frac{56}{57}\right)$$ $$e\left(\frac{37}{57}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{8}{57}\right)$$ $$e\left(\frac{23}{57}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{55}{57}\right)$$ $$e\left(\frac{14}{57}\right)$$ $$e\left(\frac{49}{57}\right)$$
$$\chi_{4011}(26,\cdot)$$ 4011.ck 570 yes $$1$$ $$1$$ $$e\left(\frac{167}{570}\right)$$ $$e\left(\frac{167}{285}\right)$$ $$e\left(\frac{41}{57}\right)$$ $$e\left(\frac{167}{190}\right)$$ $$e\left(\frac{7}{570}\right)$$ $$e\left(\frac{71}{114}\right)$$ $$e\left(\frac{87}{190}\right)$$ $$e\left(\frac{49}{285}\right)$$ $$e\left(\frac{227}{285}\right)$$ $$e\left(\frac{563}{570}\right)$$
$$\chi_{4011}(29,\cdot)$$ 4011.bz 190 no $$1$$ $$1$$ $$e\left(\frac{27}{190}\right)$$ $$e\left(\frac{27}{95}\right)$$ $$e\left(\frac{7}{38}\right)$$ $$e\left(\frac{81}{190}\right)$$ $$e\left(\frac{31}{95}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{43}{95}\right)$$ $$e\left(\frac{54}{95}\right)$$ $$e\left(\frac{99}{190}\right)$$ $$e\left(\frac{33}{190}\right)$$
$$\chi_{4011}(31,\cdot)$$ 4011.bu 114 no $$1$$ $$1$$ $$e\left(\frac{49}{57}\right)$$ $$e\left(\frac{41}{57}\right)$$ $$e\left(\frac{101}{114}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{85}{114}\right)$$ $$e\left(\frac{109}{114}\right)$$ $$e\left(\frac{25}{38}\right)$$ $$e\left(\frac{25}{57}\right)$$ $$e\left(\frac{49}{114}\right)$$ $$e\left(\frac{43}{57}\right)$$
$$\chi_{4011}(32,\cdot)$$ 4011.bq 114 yes $$-1$$ $$1$$ $$e\left(\frac{89}{114}\right)$$ $$e\left(\frac{32}{57}\right)$$ $$e\left(\frac{83}{114}\right)$$ $$e\left(\frac{13}{38}\right)$$ $$e\left(\frac{29}{57}\right)$$ $$e\left(\frac{67}{114}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{7}{57}\right)$$ $$e\left(\frac{73}{114}\right)$$ $$e\left(\frac{28}{57}\right)$$
$$\chi_{4011}(34,\cdot)$$ 4011.cc 190 no $$-1$$ $$1$$ $$e\left(\frac{84}{95}\right)$$ $$e\left(\frac{73}{95}\right)$$ $$e\left(\frac{33}{38}\right)$$ $$e\left(\frac{62}{95}\right)$$ $$e\left(\frac{143}{190}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{39}{190}\right)$$ $$e\left(\frac{51}{95}\right)$$ $$e\left(\frac{141}{190}\right)$$ $$e\left(\frac{47}{190}\right)$$
$$\chi_{4011}(37,\cdot)$$ 4011.bw 114 no $$-1$$ $$1$$ $$e\left(\frac{8}{57}\right)$$ $$e\left(\frac{16}{57}\right)$$ $$e\left(\frac{35}{57}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{43}{57}\right)$$ $$e\left(\frac{5}{114}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{32}{57}\right)$$ $$e\left(\frac{4}{57}\right)$$ $$e\left(\frac{85}{114}\right)$$
$$\chi_{4011}(38,\cdot)$$ 4011.bt 114 yes $$-1$$ $$1$$ $$e\left(\frac{29}{114}\right)$$ $$e\left(\frac{29}{57}\right)$$ $$e\left(\frac{10}{57}\right)$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{49}{114}\right)$$ $$e\left(\frac{17}{57}\right)$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{1}{57}\right)$$ $$e\left(\frac{50}{57}\right)$$ $$e\left(\frac{4}{57}\right)$$
$$\chi_{4011}(40,\cdot)$$ 4011.cg 570 no $$-1$$ $$1$$ $$e\left(\frac{232}{285}\right)$$ $$e\left(\frac{179}{285}\right)$$ $$e\left(\frac{7}{114}\right)$$ $$e\left(\frac{42}{95}\right)$$ $$e\left(\frac{499}{570}\right)$$ $$e\left(\frac{43}{57}\right)$$ $$e\left(\frac{149}{190}\right)$$ $$e\left(\frac{73}{285}\right)$$ $$e\left(\frac{403}{570}\right)$$ $$e\left(\frac{71}{570}\right)$$
$$\chi_{4011}(41,\cdot)$$ 4011.bk 38 yes $$-1$$ $$1$$ $$e\left(\frac{27}{38}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{5}{38}\right)$$ $$e\left(\frac{5}{38}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$
$$\chi_{4011}(43,\cdot)$$ 4011.bp 95 no $$1$$ $$1$$ $$e\left(\frac{81}{95}\right)$$ $$e\left(\frac{67}{95}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{53}{95}\right)$$ $$e\left(\frac{91}{95}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{68}{95}\right)$$ $$e\left(\frac{39}{95}\right)$$ $$e\left(\frac{12}{95}\right)$$ $$e\left(\frac{4}{95}\right)$$
$$\chi_{4011}(44,\cdot)$$ 4011.cj 570 yes $$1$$ $$1$$ $$e\left(\frac{131}{570}\right)$$ $$e\left(\frac{131}{285}\right)$$ $$e\left(\frac{79}{114}\right)$$ $$e\left(\frac{131}{190}\right)$$ $$e\left(\frac{263}{285}\right)$$ $$e\left(\frac{13}{57}\right)$$ $$e\left(\frac{93}{95}\right)$$ $$e\left(\frac{262}{285}\right)$$ $$e\left(\frac{37}{570}\right)$$ $$e\left(\frac{329}{570}\right)$$
$$\chi_{4011}(46,\cdot)$$ 4011.ce 285 no $$1$$ $$1$$ $$e\left(\frac{158}{285}\right)$$ $$e\left(\frac{31}{285}\right)$$ $$e\left(\frac{10}{57}\right)$$ $$e\left(\frac{63}{95}\right)$$ $$e\left(\frac{208}{285}\right)$$ $$e\left(\frac{17}{57}\right)$$ $$e\left(\frac{88}{95}\right)$$ $$e\left(\frac{62}{285}\right)$$ $$e\left(\frac{136}{285}\right)$$ $$e\left(\frac{77}{285}\right)$$
$$\chi_{4011}(47,\cdot)$$ 4011.cl 570 yes $$-1$$ $$1$$ $$e\left(\frac{371}{570}\right)$$ $$e\left(\frac{86}{285}\right)$$ $$e\left(\frac{2}{57}\right)$$ $$e\left(\frac{181}{190}\right)$$ $$e\left(\frac{391}{570}\right)$$ $$e\left(\frac{49}{57}\right)$$ $$e\left(\frac{1}{190}\right)$$ $$e\left(\frac{172}{285}\right)$$ $$e\left(\frac{221}{285}\right)$$ $$e\left(\frac{232}{285}\right)$$
$$\chi_{4011}(50,\cdot)$$ 4011.ca 190 no $$-1$$ $$1$$ $$e\left(\frac{161}{190}\right)$$ $$e\left(\frac{66}{95}\right)$$ $$e\left(\frac{15}{38}\right)$$ $$e\left(\frac{103}{190}\right)$$ $$e\left(\frac{23}{95}\right)$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{84}{95}\right)$$ $$e\left(\frac{37}{95}\right)$$ $$e\left(\frac{147}{190}\right)$$ $$e\left(\frac{72}{95}\right)$$
$$\chi_{4011}(52,\cdot)$$ 4011.bv 114 no $$-1$$ $$1$$ $$e\left(\frac{37}{57}\right)$$ $$e\left(\frac{17}{57}\right)$$ $$e\left(\frac{53}{114}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{13}{114}\right)$$ $$e\left(\frac{8}{57}\right)$$ $$e\left(\frac{15}{38}\right)$$ $$e\left(\frac{34}{57}\right)$$ $$e\left(\frac{37}{114}\right)$$ $$e\left(\frac{101}{114}\right)$$
$$\chi_{4011}(53,\cdot)$$ 4011.cj 570 yes $$1$$ $$1$$ $$e\left(\frac{523}{570}\right)$$ $$e\left(\frac{238}{285}\right)$$ $$e\left(\frac{23}{114}\right)$$ $$e\left(\frac{143}{190}\right)$$ $$e\left(\frac{34}{285}\right)$$ $$e\left(\frac{11}{57}\right)$$ $$e\left(\frac{29}{95}\right)$$ $$e\left(\frac{191}{285}\right)$$ $$e\left(\frac{461}{570}\right)$$ $$e\left(\frac{217}{570}\right)$$
$$\chi_{4011}(55,\cdot)$$ 4011.bj 38 no $$1$$ $$1$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{11}{38}\right)$$ $$e\left(\frac{15}{38}\right)$$ $$e\left(\frac{3}{38}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{5}{38}\right)$$ $$e\left(\frac{4}{19}\right)$$